The \arrowhead torus" is a broadcast graph that we deene on the 6-valent grid as a Cayley graph. We borrow the term from Mandelbrot who qualiies in that way one of the Sierpinski's famous fractal constructions. The 6-valent grid H = (V; E) is generated by three families of straight lines. We adopt the isotropic orientation S ! N, NE ! SW, NW ! SE and deene the system of generators S = fs 1 ; s ...

For a positive integer n, does there exist a vertex-transitive graph r on n vertices which is not a Cayley graph, or, equivalently, a graph r on n vertices such that Aut F is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, MaruSic and Scapellato, and McKay and the second author) has produced answers to ...

We present a formulation of the Cayley-Hamilton theorem for hypermatrices in conjunction with the corresponding combinatorial interpretation. Finally we discuss how the formulation of the Cayley-Hamilton theorem for hyermatrices leads to new graph invariants which in some cases results in symmetry breakings among cospectral graphs.

In this paper we introduce a new class of double coset Cayley digraphs induced by quasigroups. These graphs can be considered as the generalization of Double Coset Cayley Digraphs induced by loops. Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature.

We investigate the existence of Hamilton paths in connected Cayley graphs on generalized dihedral groups. In particular, we show that a connected Cayley graph of valency at least three on a generalized dihedral group, whose order is divisible by four, is Hamiltonconnected, unless it is bipartite, in which case it is Hamilton-laceable.

Vadapalli and Srimani [2] have proposed a new family of Cayley graph interconnection networks of constant degree four. Our comments show that their proposed graph is not new but is the same as the wrap-around butterfly graph. The structural kinship of the proposed graph with the de Bruijn graph is also discussed.

We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For 2-automatic sequences, we find a characterization in terms of what we call homogeneity, and among homogeneous sequences, we single out those enjoying what we call self-similarity. It turns out that self-similar 2-automatic sequences (viewed up to a permutation ...

Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat corresponding for Cayley over semi-dihedral group SD8n = ?a,b | a4n b2 1; bab a2n-1?, n ? 2. We present several necessary sufficient conditions integrality SD8n, also obtain some simple terms Boolean algebra hai. particular, give groups SD2n (n?4)...

This paper demonstrates the power of the Cayley graph approach to solve specific applications , such as rearrangement problems and the design of interconnection networks for parallel CPU's. Recent results of the authors for efficient use of Cayley graphs are used here in exploratory analysis to extend recent results of Babai et al. on a family of trivalent Cayley graphs associated with P SL 2 (...

A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group K o H such that S = a for some a ∈ K with 〈a〉 = K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as ...